This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the step-by-step solution for factoring the quadratic expression 12x^2 - 13x - 14: Step 1: Identify the coefficients and find two numbers that multiply to a × c and add to b. For 12x^2 - 13x - 14, we have a=12, b=-13, c=-14. We need two numbers that multiply to a × c = 12 × (-14) = -168 and add up to b = -13. These numbers are 8 and -21. (8 × -21 = -168 and 8 + (-21) = -13) Step 2: Rewrite the middle term using the two numbers found in Step 1. 12x^2 + 8x - 21x - 14 Step 3: Group the terms and factor out the greatest common factor (GCF) from each pair. 4x(3x + 2) - 7(3x + 2) Step 4: Factor out the common binomial factor. (4x - 7)(3x + 2) The final factored expression is: (4x - 7)(3x + 2) Last free one today — make it count tomorrow, or type /upgrade for unlimited.